Risk Management with Probability: Kelly Criterion, VaR & Crash Detection

The Indicator That Tells You When NOT to Trade

Most indicators focus on finding entries. AIO Prediction Market Simulator does something fundamentally different: it computes the probability of price reaching specific targets and uses that to generate BUY/SHORT/WAIT/AVOID decisions. The WAIT and AVOID states are arguably the most valuable signals — knowing when to stay out is the essence of risk management.

Kelly Criterion: Optimal Position Sizing

The Kelly Criterion is the mathematically optimal formula for position sizing given an edge:

f* = (p × b - q) / b

Where:

• p = probability of winning (from Monte Carlo simulation)
• q = probability of losing (1 - p)
• b = ratio of win amount to loss amount
• f* = fraction of capital to risk

Why Fractional Kelly?

Full Kelly is mathematically optimal but produces extreme drawdowns. A 50% drawdown is common under full Kelly. AIO uses fractional Kelly (default 15% of full Kelly for crypto, higher for less volatile markets), which sacrifices some return for dramatically smoother equity curves.

The indicator automatically adjusts the fractional Kelly based on Market Type preset:

• Crypto: 15% Kelly (very conservative — high volatility)
• Stocks: 25% Kelly
• Forex: 30% Kelly
• Bonds: 40% Kelly (lowest volatility)

Value at Risk (VaR) & Expected Shortfall

VaR answers: “What’s the worst-case loss I should expect with X% confidence over Y period?”

AIO computes VaR directly from Monte Carlo paths:

• VaR 95%: The 5th-percentile outcome from 1,500 simulated price paths. “Only 5% of scenarios are worse than this.”
• VaR 99%: The 1st-percentile outcome. Extreme downside.
• Expected Shortfall (CVaR): The average of all scenarios worse than VaR. While VaR tells you the boundary, ES tells you how bad it gets if that boundary is crossed.

Crash Probability via Importance Sampling

Standard Monte Carlo is terrible at estimating rare events. Running 1,500 simulations, a 2% crash probability means only ~30 paths actually crash — too few for reliable estimation.

AIO solves this with Importance Sampling — a technique from quantitative finance:

1. Tilt the sampling distribution: Instead of sampling from the real-world distribution, sample from a shifted distribution that makes crashes more likely ($\mu$ shifted down by the crash threshold)
2. Run simulations: More crash scenarios are generated
3. Reweight results: Each path’s probability is adjusted by the likelihood ratio (how much more likely the tilted distribution made this path vs the real distribution)
4. Result: Crash probability estimated with 10-100× more effective samples

The crash threshold is calibrated per Market Type (crypto default: 5% crash in 1 day; stocks: 3%).

Particle Filter: Bayesian Probability Updating

While Monte Carlo provides a forward-looking probability estimate, the Particle Filter provides a backward-looking one that updates with each new bar:

1. Propagate: 200 particles simulate possible future states based on process volatility
2. Reweight: Each particle is scored by how well it predicted the actual observed price (exponential weighting based on observation noise)
3. Resample: Particles with low weights are eliminated; high-weight particles are duplicated (systematic resampling)
4. Estimate: The weighted average probability from all particles gives the PF probability

The Particle Filter acts as a second opinion to Monte Carlo. When both agree, confidence is highest.

The 4-Signal Decision Engine

All these components feed into a simple decision framework:

1. MC Signal: Is the stronger Monte Carlo probability >33%?
2. PF Agreement: Does the Particle Filter agree (>54%)?
3. Bias Edge: Is there a measurable edge (>5% difference between bull and bear)?
4. Model Convergence: Do Monte Carlo and Black-Scholes agree within tolerance?

Decision States

• BUY / SHORT: 3-4 signals agree + crash risk acceptable → green/red marker
• BUY? / SHORT?: Only 2 signals agree → possible but uncertain
• WAIT: Crash risk moderate → orange marker — stay out
• AVOID: Crash risk severe → dark red marker — close positions

Brier Score: Is the Model Working?

Every N bars (configurable), the indicator records its probability prediction and later evaluates whether the outcome matched. The Brier Score measures calibration quality:

• Brier < 0.15: Excellent calibration — model predictions are reliable
• Brier 0.15-0.25: Acceptable — model provides useful edge
• Brier > 0.25: Poor — model may need parameter adjustment or market regime has changed

This is self-auditing — the indicator tells you when its own predictions are degrading, something no other TradingView indicator does.

Practical Risk Management Workflow

1. Check Decision State: Only trade when state is BUY or SHORT (not WAIT/AVOID)
2. Check Crash Probability: If crash prob > 6%, reduce position or stay flat
3. Set position size using Kelly % (shown in the info table)
4. Set stop loss at VaR 95% level
5. Check Brier Score: If >0.25, reduce conviction and position size by 50%
6. Use signal alerts: “WAIT/AVOID → BUY/SHORT” transition alerts catch the exact moment conditions improve